When fighting fizz, you should make sure you don't die to him while also hoping to high heaven that your allies listen to your MIA pings, because as soon as he picks up a single kill, he'll be able to 100-0 you without using his entire kit. He was easier to outplay when ahead when towers actually hurt and the current keystones didn't exist.
More seriously? Fizz is an Assassin, and like any assassin, he snowballs super easy but struggles to deal any damage if he's behind. I've won more than a few fizz lanes as my main mid Lux, though that's also reliant on not dying early or having him pick up kills from a roam - but that's asking a lot from bronze-gold.
General advice I can provide is this - zone him as hard as you can, attack him with autos or abilities whenever he goes in to last hit - though remember you also want the wave near your turret. In addition, his Q - the spear dash is targeted against a unit or champion, so be aware that your own minions are potentially a source of mobility for him, and that if he DOES pass through you using it, his next E is going to hurt a TON. On another note, it does put you on the other side. Do keep in mind, however, that if you're even, his damage is still pretty disgusting.
Rushing an Hourglass might be an idea, though since his main source of damage is AP, it isn't quite as effective as it is against Zed/Yasuo/Talon, and having a runepage with flat MR blues, and maybe MR quints if you're wanting to feel extra safe might be an idea. Also, depending on your champion, rushing an abyssal might be a valid choice.
On the other end, Riot could probably improve clarity when playing against him, but having that little trident icon be visible to his opponents as well, just like how they should show the timers on the minions Yas has E'd through.
